Heretofore, modulation and demodulation systems of 32 Quadrature Amplitude Modulation (QAM) and 128 QAM have been adopted in a digital microwave communication system. Further, application of the 32 QAM system has been mainly suggested in a mobile communication system. There is an example in which the 32 QAM is described for standardization as a modulation element of adaptive modulation and coding. Moreover, there is also a standard utilizing the 32 QAM in digital video broadcasting (DVB).
As such a modulation and demodulation system, for example, Japanese Patent Application Publication No. 2003-179657 (Patent Document 1) discloses a configuration that required back-off is generated by controlling the magnitude of a digital signal in a stage prior to a modulator by the adaptive modulation. However, an error rate is not good in the configuration.
Further, Japanese Patent Application Publication No. 2-113753 (Patent Document 2) discloses a configuration of a mapping circuit capable of utilizing a common circuit by repeating eight signal points as a unit of 3 bits in a code modulation circuit that can change a multilevel value between 16, 32 and 64. However, the mapping is based on a specific code modulation. An error rate cannot be improved unless an error correction coding is applied thereto.
Moreover, Japanese Patent Application Publication No. 11-205402 (Patent Document 3) discloses a configuration in which a 128 QAM system is generated by arranging four 32 QAM systems on four quadrants. However, an error rate is not good.
Furthermore, Japanese Patent Application Publication No. 2001-127809 (Patent Document 4) and Japanese Patent Application Publication No. 6-326742 (Patent Document 5) discloses mapping of a multilevel code in 32 QAM. However, the mapping is directed to the multilevel code. An error rate cannot be improved unless an error correction coding is applied thereto.
The four conventional techniques described above are configured to be based on code modulation or multilevel coding. In these types of code modulation, the amount of information transmitted by one symbol decreases greater than a logarithm of a multilevel value having 2 as a base. In addition, these types of mapping are not suitable for application of another simple error correction coding. Further, encoding is required that an average Hamming distance becomes a minimum value in order to apply a simple error correction code such as a block code.
As a technique cited in learned journals, there is 32 QAM mapping disclosed in, for example, J. Smith, “Odd-Bit Quadrature Amplitude-Shift Keying,” IEEE Trans. Commun., vol. 23, Issue 3, pp. 385-389, March 1975. (Non-Patent Document 1) and P. K. Vifthaladevuni, and M.-S. Alouini, “Exact BER computation for the cross 32-QAM constellation,” Proc. ISCCS, pp. 643-646, 2004 (Non-Patent Document 2). FIG. 10 is mapping utilized in the Non-Patent Documents 1, 2. In this 32 QAM mapping, an error rate characteristic P(γ) is expressed in the following expression (1) as an approximate expression under Q(x)<<1, where γ indicates a noise power ratio to carrier wave power.
                                          P            ⁡                          (              γ              )                                =                                    3              4                        ⁢                          Q              ⁡                              (                                                      γ                    10                                                  )                                                    ⁢                                  ⁢                  Here          ,                                    (        1        )                                          Q          ⁡                      (            x            )                          =                              1                                          2                ⁢                                                                  ⁢                π                                              ⁢                                    ∫              x              ∞                        ⁢                                          ⅇ                                                      -                                          t                      2                                                        /                  2                                            ⁢                                                          ⁢                              ⅆ                t                                                                        (        2        )            
Although the 32 QAM transmits 5 bits by one symbol, in the mapping utilized in the Non-Patent Documents 1, 2, as shown in FIG. 10, 4 bits of the 5 bits are merely symmetrical with respect to an x axis, whereby it is impossible to apply a differential encoding against 90-degree phase uncertainty of a reproduced carrier wave thereto.
As a first conventional technique defined by standardization, there is a standard of Digital Video Broadcasting (DVB) of the European Telecommunications Standards Institute (ETSI), and there can be mentioned 32 QAM mapping disclosed in EN 300 429 V1.2.1, “Digital Video Broadcasting (DVB); Framing Structure, Channel coding and modulation for cable systems,” April 1998 (Non-Patent Document 3). FIG. 11 is mapping utilized in the Non-Patent Document 3. In this mapping, an error rate characteristic P(γ) is expressed in the following expression (3) as an approximate expression under Q(x)<<1, where γ indicates a noise power ratio to carrier wave power.
                              P          ⁡                      (            γ            )                          =                              11            10                    ⁢                      Q            ⁡                          (                                                γ                  10                                            )                                                          (        3        )            
In the mapping utilized in the Non-Patent Document 3, as shown in FIG. 11, 3 bits of the 5 bits are rotationally symmetrical, and 2 bits of the 3 bits are a quadrant signal. Thus, it is possible to apply a differential encoding against 90-degree phase uncertainty of a reproduced carrier wave thereto.
As a second conventional technique defined by standardization, there is a standard of Personal Handyphone System, PHS, (second-generation cordless telephone system), and there can be mentioned 32 QAM mapping disclosed in Association of Radio Industries and Businesses (ARIB), “second-generation cordless telephone system standards (first volume)/(second volume)” RCR STD-28-1/RCR STD-28-2, March 2002 (Non-Patent Document 4). FIG. 12 is mapping utilized in the Non-Patent Document 4. In this mapping, an error rate characteristic P(γ) is expressed in the following expression (4) as an approximate expression under Q(x)<<1, where γ indicates a noise power ratio to carrier wave power.
                              P          ⁡                      (            γ            )                          =                              8            5                    ⁢                      Q            ⁡                          (                                                γ                  10                                            )                                                          (        4        )            
In the mapping of this conventional technique, as shown in FIG. 12, 3 bits of the 5 bits are symmetrical with respect to an axis, and 2 bits are symmetrical with respect to the axis in reverse. Therefore, it is impossible to apply a differential encoding against 90-degree phase uncertainty of a reproduced carrier wave thereto.
In the conventional techniques disclosed in the above Non-Patent Documents 3, 4, because an average Hamming distance between adjacent signal points does not become a minimum, the number of bit errors per a symbol error does not necessarily become a minimum. Thus, it is impossible to improve the error rate. Further, since it is the mapping that generates 3 bits or 4 bits of the bit error per 1 symbol error, it is hard to say that bit errors per 1 symbol error can be made as small as possible.
With respect to such a problem, it is possible to improve the error rate by the techniques disclosed in the Non-Patent Documents 1, 2.
However, in the techniques disclosed in the Non-Patent Documents 1, 2, as shown in FIG. 10, a bit at a left lower position of upper-side 3 bits and lower-side 2 bits in a binary signal becomes “1” when a Y axis is positive, and the bit becomes “0” when the Y axis is negative. Therefore, it can merely deal with phase uncertainty of 180 degrees, and it is only possible to apply a differential operation modulo 2 thereto.
Generally, in a multilevel QAM system in which a multilevel value is an odd power of 2, occurrence possibility of each signal point is set to equality, and an absolute phase is not transmitted. Thus, geometric arrangement of the signal points has symmetry of 90 degrees, and a phase of a reproduced carrier wave at a receiving side has uncertainty of 90 degrees. This can be understood that the signal points are superimposed by rotating the signal points by 90 degrees. However, in the techniques disclosed in the Non-Patent Documents 1, 2, it is merely possible to apply a differential operation modulo 2 thereto. Thus, there is a problem that only one bit can be caused to pass through with respect to drawing phases of 0 degree and 180 degrees of uncertainty of four phases, but all signals cannot necessarily be caused to pass thorough with respect to phase uncertainty of 90 degrees and 270 degrees.